Problem 2 (30 points): A small barbershop, operated by a single barber, has room for at most three customers. Potential customers arrive according to a Poisson process with rate three customers per hour, and the customer service times are exponentially distributed with a mean of 15 minutes. Cus- tomers who find the shop full, walk away. i. (5 pts) Model the operation of this barbershop as a Markovian queue- ing station. What is the classification of this station in the Kendall notation? ii. (5 pts) Argue that the operation of the queueing station that is defined in part (i) is stable, and that the barbershop will reach a "steady-state" operational regime. iii. (5 pts) What is the average number of customers in this barbershop at steady-state? iv. (5 pts) What is the percentage of arriving customers that will actually receive service, when the barbershop operates in steady-state? v. (5 pts) What is the expected waiting time for a customer who enters the barbershop under operation in steady-state? vi. (5 pts) What is the expected total time in the barbershop for a cus- tomer who enters the barbershop under operation in steady-state?